1. Field of the Invention
The present invention relates to a computer simulation method for a manufacturing process of a semiconductor device, and in particular to a computer simulation method of a surface shape of a semiconductor device using a modified cell model during etching and growth of the device.
2. Description of the Background Art
In a manufacturing process of a semiconductor device, there have been generally used two computer simulation methods for modeling a geometrical surface shape of the semiconductor device and predicting its varied surface shape during etching or growth. One method is a cell model considering the entire material to be etched or deposited, and the other method is a string model considering merely a surface of the material to be etched or deposited.
First, the cell model will now be described. In the cell model, the entire material to be etched or deposited is divided into square-shaped cells of a predetermined size. In the case of etching, the time for each cell to be removed depends upon the number of exposed sides and an etching speed of the cells. FIG. 1 is a cross-sectional view illustrating an etching computer simulation using the cell model. Reference numerals 0, 1 and 2 denote the air in an etching chamber, a semiconductor substrate, respectively. That is, as depicted in FIG. 1, a hole is formed by etching the semiconductor device 1 using the mask 2. As shown therein, etching is carried out along a surface consisting of the cells which are not etched and located closely to the etched cells. As a cell is removed by etching, another cell is exposed. In the cell model, the smaller the size of cell is, the higher the resolution is. As a result of smaller cell size, the accuracy of the computer simulation is improved, but the computation time is increased. Accordingly, it is required to properly adjust the accuracy and computation time.
Therefore, there is a disadvantage in that obtaining a more accurate result takes a longer time and requires a large amount of memory. Also the entire material considering a depth, in addition to the surface to be etched or deposited is divided into cells, and all information regarding the cells is stored, thus requiring the large amount of memory. It is thus inefficient because of a longer computation time.
Second, the string model which is another conventional computer simulation method, will now be explained. FIG. 2 is a cross-sectional view illustrating a step of computer simulation of a material surface during etching using the string model. In the case of the string model, etching points are determined at certain intervals along the surface to be etched, and are moved at certain intervals of time by a distance computed by an etching speed. FIG. 2 illustrates a section before the etching 3 and a section after the etching 4 on which the computer simulation is carried out. As depicted in FIG. 2, there are the etching points (X) at the section before the etching 3 positioned at certain intervals of time. When the computer simulation is performed, the etching points (X) are moved at certain intervals of time, thereby obtaining moved etching points (Xxe2x80x2). The moved etching points (Xxe2x80x2) are connected by straight lines, thereby obtaining the surface after etching 4. As illustrated in FIG. 2, each string at the etching sections has a different etching speed and direction according to its surface angles. It is presumed that a vector taking the etching speed and etching direction as its size and direction, respectively, is a motion vector of each string. The motion vector of the etching point where two strings. Meet each other is defined as a sum of the motion vectors of the two adjacent strings. The string is reconstituted by connecting the moved etching points obtained by the sums of the motion vectors in respect of each etching point. If the string is too long, it is shortened to a proper length by a remeshing operation.
The computation time of the above-described string model is faster than the cell model. The computation times of the computer simulations each respectively employing the cell models of different density and the string model are compared in Table I.
As discussed earlier, in the case of the cell model, the more the cell density increases, the more demand upon the central processing unit (CPU) is increased. As a result, the computation time is also increased. Also, although the string model is faster in computation than the cell model, it has several disadvantages. In the light of the etching, the string model has the following disadvantages.
First, in determining an interval of the etching point, namely a string length, a surface shape is possibly described merely with a small number of strings when the surface is flat. However, in the case of an uneven surface, a great many of strings are required to exactly describe a geometrical surface shape, which results in an increase of the computation time.
Second, when the etching speed is sharply changed, if the time interval of moving the etching point, namely the interval of etching time if not very small, it is impossible to exactly describe a shape of the etching section according to the rapid change of the etching speed. Accordingly, the shape of the section after completing the computer simulation may be remarkably different from the actual shape of the etching section. In addition, if the interval of etching time updating is shortened for the accuracy of the computer simulation a large amount of memory is necessary, and the computation time is increased.
Third, when the interval of etching time and the string length are not appropriate, or when the etching speed is sharply changed according to the position, the strings may become tangled with one another, thus forming a loop. FIG. 3a depicts a loop formed by connecting the moved etching points, when the interval of etching time is large, and the etching points have severely different movement direction and movement size. The loop does not accurately describe the actual etched section, and thus must be removed by a delooping operation, as illustrated in FIG. 3b. The de-looping operation designates an intersect point of the strings re-constituted by the moved etching points as a new etching point, and then removes the loop. Accordingly, the string model has a disadvantage in that it requires such a loop removal process, thus complicating the computation process.
It is therefore an object of the present invention to provide an improved computer simulation method employing a modified cell mainly having the properties of a cell model and additionally having those of a string model, which can obtain an accurate computation result and a rapid computation speed, and can prevent a loop from occurring.
In order to achieve the above-described object of the present invention, in a growth or etching computer simulation method dividing a material to be deposited or etched into cells in a predetermined size, and simulating a surface shape of the material after carrying out the growth or etching for a time T, the growth or etching computer simulation method using a modified cell model, includes: forming an initial section of the material with open cells among the cells exposed to the growth or etching; inputting information including growth or etching points into each open cell; computing a movement speed for the growth of etching points; moving the growth or etching points for a time determined according to the movement speed; forming a new etching section by re-arranging the open cells exposed to the growth or etching, after moving the growth or etching points, such steps being repeatedly performed on the re-arranged open cells until the sum of the predetermined time reaches the time (T).